Algorithm on Higher-Order Derivative Based on Ternary Optical Computer

Abstract

As an important tool in the field of mathematics, higher-order derivation problems are widely used in differentials, quantum mechanics, and engineering applications. However, in the electronic computer (EC), due to the existence of the carry in the calculation, the computational efficiency is low when solving the higher-order derivation problem. In response to this problem, the ternary optical computer (TOC) has the advantages of no carry-in and the characteristics of numerous data bits, reconfigurable processors and parallel computing. Solve the higher-order derivation problems with complex operations by constructing multipliers and adders on the TOC platform, and copying multiple composite operator units (COUs). This article introduces the design of the higher-order derivative algorithm based on TOC in detail, the reconfiguration process of the multiplier and adder, and the number of bits of the multiplier and adder required in the implementation is given. Besides, the hardware resources and clock cycles in the operation are analyzed. The feasibility of the implementation scheme is verified by experiments. Compared with the traditional higher-order derivative, the higher-order derivative based on the TOC is superior in time performance, computational efficiency, and processing of complex operations. Due to the limitation of the research stage, the algorithm is only applicable to the function of polynomials, which lays a foundation for the further research of higher-order derivative algorithms, and has certain application significance.

Keywords

• Ternary optical computer
• higher-order derivative
• MSD adder
• MSD multiplier
• composite operator unit